I've been getting big blood clots during my period. Is this normal?

Can be... If this is a change from your normal menstrual cycle please discuss this with your gyn; or primary care physician.
Maybe. Women can get clots in their period on their heaviest days of bleeding, which is normal. However, regular heavy periods with lots of clotting are abnormal and can be caused by changes in the uterus, including endometriosis, ovarian cysts, miscarriage, fibroids, or a change in hormone balance. See your doctor if you are experiencing frequent clots or very heavy bleeding.
No, U Have Options. Depends on cause of heavy bleeding. Need evaluation and sonogram. Non-surgical options include: birth control pills. Lysteda (non-hormonal rx taken during period), Mirena (levonorgestrel) iud. Minimally invasive options: endometrial ablation (in-office), hysteroscopy polyp removal or fibroid resection; and only if these treatments fail then consider hysterectomy - vaginal or laparoscopic if possible.
Sometimes. Some women have heavier periods and blood clots. Most women don't. So it depends on if that is normal for you or a change. It may be a good idea to see your gyn to make sure everything is ok.